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Unformatted text preview: Home > My Assignments > Section 7.3 (Homework) About this Assignment SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University Due: Tuesday, October 18, 2005 11:02 PM EDT Description Separable Equations Current Score: 11.5 out of 15.5 Question Score pts 1 1/1 2 1/1 3 1/1 3/3 Viewing: Last Response View: All Responses Notes subs 2/20 2/20 2/20 1. [SCalcCC2 7.3.02.] Solve the differential equation. Give your answer using the form below where Z is an arbitrary positive constant. A = 3 [3] B = 1/7 [0.143] C = 7 [7] 2. [SCalcCC2 7.3.04.] Solve the differential equation using K as your arbitrary constant. y' = xy y(x) = K*exp(x^2/2) [K*exp(x^2/2)] pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 -/3 -/20 Notes 3. [SCalcCC2 7.3.08.] Solve the differential equation. Let C represent an arbitrary constant. (Note: In this case, WebAssign expects your answer to have a negative sign in front of the arbitrary C.) z = (No Response) pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 0.5/0.5 5/20 0.5/0.5 Viewing: Last Response View: All Responses Notes [-ln(exp(t) - C)] 4. [SCalcCC2 7.3.12.] Find the solution of the differential equation that satisfies the given initial condition. y = sqrt(-sqrt((x^2)+1)+2) [sqrt(2 - sqrt(x^2+1))] 5. [SCalcCC2 7.3.24.] Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. x2 - y2 = k (o) (o) This is a family of hyperbolas. (_) (_) This is a family of ellipses. (_) (_) This is a family of straight lines. (_) (_) This is a family of concentric circles. (_) (_) This is a family of parabolas. pts subs 1 2/2 1/20 2 -/1 -/20 2/3 Viewing: Last Response View: All Responses Notes 6. [SCalcCC2 7.3.36.] A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. (a) How much salt is in the tank after t minutes? (130/3)*(1-exp(-3*t/200)) kg [(130/3)*(1-exp(-3*t/200))] (b) How much salt is in the tank after 40 minutes? (No Response)[19.6] kg Home My Assignments Home > My Assignments > Section 7.3 (Homework) SMALL BRIAN DIXON MA 241, section 009, Fall 2005 Instructor: Drew Pasteur North Carolina State University About this Assignment Due: Tuesday, October 18, 2005 11:02 PM EDT Description Separable Equations Current Score: 11.5 out of 15.5 Question Score pts 1 1/1 2 1/1 3 1/1 3/3 Viewing: Last Response View: All Responses Notes subs 2/20 2/20 2/20 1. [SCalcCC2 7.3.02.] Solve the differential equation. Give your answer using the form below where Z is an arbitrary positive constant. A = 3 [3] B = 1/7 [0.143] C = 7 [7] 2. [SCalcCC2 7.3.04.] Solve the differential equation using K as your arbitrary constant. y' = xy y(x) = K*exp(x^2/2) [K*exp(x^2/2)] pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 -/3 -/20 Notes 3. [SCalcCC2 7.3.08.] Solve the differential equation. Let C represent an arbitrary constant. (Note: In this case, WebAssign expects your answer to have a negative sign in front of the arbitrary C.) z = (No Response) [-ln(exp(t) - C)] pts subs 1 3/3 1/20 3/3 Viewing: Last Response View: All Responses Notes pts subs 1 0.5/0.5 5/20 0.5/0.5 4. [SCalcCC2 7.3.12.] Find the solution of the differential equation that satisfies the given initial condition. y = sqrt(-sqrt((x^2)+1)+2) [sqrt(2 - sqrt(x^2+1))] 5. [SCalcCC2 7.3.24.] Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen. x2 - y2 = k (o) (o) This is a family of hyperbolas. (_) (_) This is a family of ellipses. (_) (_) This is a family of straight lines. (_) (_) This is a family of concentric circles. (_) (_) This is a family of parabolas. Viewing: Last Response View: All Responses Notes pts subs 1 2/2 1/20 2 -/1 -/20 2/3 Viewing: Last Response View: All Responses Notes 6. [SCalcCC2 7.3.36.] A tank contains 1000 L of pure water. Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. (a) How much salt is in the tank after t minutes? (130/3)*(1-exp(-3*t/200)) kg [(130/3)*(1-exp(-3*t/200))] (b) How much salt is in the tank after 40 minutes? (No Response)[19.6] kg Home My Assignments ...
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This note was uploaded on 10/21/2009 for the course MATH MA241 taught by Professor Hubbard during the Spring '09 term at N.C. Central.

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